The unit circle and quadrants

The unit circle and quadrants

Replace this with a sub-header that can be in multiple lines. ​

Multiple Choice

What is the exact value of $$Cos\ 30\degree$$ ?

• $$\frac{1}{2}$$

• $$\frac{1}{\sqrt[]{2}}$$

• $$\frac{\sqrt[]{3}}{2}$$

• $$\sqrt[]{3}$$

Multiple Choice

What is the exact value of $$\tan\ 60\degree$$ ?

• $$\frac{1}{2}$$

• $$\frac{1}{\sqrt[]{2}}$$

• $$\frac{\sqrt[]{3}}{2}$$

• $$\sqrt[]{3}$$

Multiple Choice

Solve $$\sin\ \theta=\frac{\sqrt[]{2}}{2}$$

• $$\theta=\frac{\pi}{6}$$

• $$\theta=\frac{\pi}{4}$$

• $$\theta=\frac{\pi}{3}$$

• $$\theta=\frac{\pi}{2}$$

​The Sine Curve

​The Cosine Curve

​The Tan Curve

​The Quadrants

​A = ALL positive
S = SIN only positive
T = TAN only positive
C = COS only positive

​x is the key angle

​Complete the table:

Multiple Choice

$$\cos\ \theta$$ is positive in

• the 1st and 2nd quadrants

• the 1st and 3rd quadrants

• the 1st and 4th quadrants

• the 2nd and 3rd quadrants

Multiple Choice

Evaluate cos(225°)

• $$-\frac{\sqrt{2}}{2}$$

• $$\frac{\sqrt{2}}{2}$$

• $$-\frac{\sqrt{3}}{2}$$

• $$-\frac{1}{2}$$

Dropdown

What is the reference angle for $$\frac{4\pi}{3}$$ ?



Reference angle = ​

Select answer

Multiple Choice

Evaluate $$\tan\left(\frac{7\pi}{6}\right)$$  

• $$-\frac{\sqrt{3}}{2}$$  

• $$\frac{\sqrt{3}}{3}$$  
  

• $$-\frac{1}{2}$$  

• $$\sqrt{3}$$  

Dropdown

Find the exact value of the following trig expressions.





$$\sin\left(\frac{\pi}{3}\right)=$$ ​

Select answer

$$\sin\left(\frac{7\pi}{6}\right)=$$ ​ ​ ​

Select answer

$$\cos\left(\frac{5\pi}{4}\right)=$$ ​

Select answer

$$\cos\left(-\frac{\pi}{3}\right)=$$ ​

Select answer

​Example:

Dropdown

Suppose you know that for a particular angle, $$\cos\theta=\frac{4}{5}$$ . The related triangle is shown. Find



$$\sin\theta=$$ ​

Select answer

Fill in the Blank

Suppose you know that for a particular angle, $$\cos\theta=\frac{4}{5}$$ . The related triangle is shown.

Given that $$\theta$$ is in the fourth quadrant,

$$\sin\theta=$$ ____

(type your answer as a fraction)

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